In the appendix I of [1]}, Rohm and Witten first gave a
description of the differentials \(d_3\)  and \(d_5\)  for the case when
\(D=d+H_3\) . Atiyah and Segal [2]} showed a method about how to
construct the differentials in terms of Massey products, and gave a
generalization of Rohm and Witten's result: the iterated Massey
products with \(H_3\)  give (up to sign) all the higher differentials
of the spectral sequence for the twisted cohomology (see
[2]}). Mathai and Wu in [4]}
considered the general case that
\(H=\sum _{i=1}^{[\frac{n-1}{2}]}H_{2i+1}\)  and claimed, without proof,
that \(d_2=d_4=\cdots =0\) , while \(d_3\) , \(d_5\) , \(\cdots \)  are given by
the cup products with \(H_3\) , \(H_5\) , \(\cdots \)  and by the higher
Massey products with them. Motivated by the method in [2]},
we give an explicit description of the differentials in the spectral
sequence (REF ) in terms of Massey products.
